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In this paper, the power flow in electrical systems is modelled in the time domain by using Geometric Algebra and the Hilbert Transform. The use of this mathematical framework overcomes some of the limitations shown by the existing methodologies under distorted supply or unbalanced load. In such cases, the derived instantaneous active current may not be the lowest RMS current in all circuit conditions and could contain higher levels of harmonic distortion than the supply voltage. Moreover, they cannot be applied to single phase systems. The proposed method can be used for sinusoidal and non-sinusoidal power supplies, non-linear loads, single- and multi-phase systems, and it provides meaningful engineering results with a compact formulation. Several examples have been included to prove the validity of the proposed theory.